First, if you're using Ionic.Utils.Zip, you are using a very old version of DotNetZip. In older versions (v1.6 and prior) the zip file was created in a temp file folder, and then moved to the final location. This could cause what you are reporting.
The v1.9 release does not do it this way, partly because other people complained about the permissions issue.

So, I suggest that you upgrade to the v1.9 release.

AFTER YOU UPGRADE, test it again.

If after you upgrade, the problem still occurs, give me more details.

What happens if you just create a file in the directory, without using DotNetZip?

Oh ok, I see...so I added the new dll reference to my project, and I changed the namespace in my code, recompiled, but I am still having the same issue where the newly created ZIP file does not have the same permissions as it's parent folder.